PencilGo

Grade 9 · Math · Algebra 1

9th grade The counting principle, and are these events independent? worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

The counting principle, and are these events independent?

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. Luz's outfit is a top (one of 6 shirts or 4 sweaters) in one of 3 colors, plus a bag (one of 5 backpacks or 2 totes). How many different outfits are possible?

  2. A 4-letter code uses the letters A to H, with no letter used twice and no vowels (A and E) allowed. Ren counts the codes. How many are possible?

  3. Tala lines up 5 kids for a photo. Zee must stand first or last. In how many different orders can the kids line up?

  4. A quiz team picks a captain and a different co-captain from n players, and there are 306 ways to do it. How many players are on Luz's team?

  5. At Milo's school, events A and B are independent. P(A) = p, P(B) = p + 0.2, and P(A and B) = 0.15. What is P(A), as a fraction in simplest form?

  6. At Noah's school, events A and B are independent. The chance A does not happen is 2/5, and P(A and B) = 3/10. What is P(B), in simplest form?

  7. On Kira's two spinners with equal parts, events A and B are independent and P(A) = P(B). The chance of both is 4/25. What is P(A), in simplest form?

  8. Read this first

    Use this

    Two-way table of 120 students. Plays a sport and has a job: 12. Plays a sport, no job: 36. No sport, has a job: 18. No sport, no job: 54.

  9. Milo surveyed 120 students and made the two-way table. A is “plays a sport” and B is “has a job”. For a random student, are A and B independent?

    • Not independent: students with jobs have less time for sports
    • Not independent: 48 × 30 = 1,440, not 12
    • Independent: 48/120 × 30/120 = 12/120, the share with both
    • Not independent: 48/120 + 30/120 is not 12/120

  10. Use this

    Two-way table of 100 students. Eats lunch at school and joins a club: 28. Eats lunch at school, no club: 42. Does not eat lunch at school, joins a club: 12. Does not eat lunch at school, no club: 18.

  11. Pia surveyed 100 students and made the two-way table. A is “eats lunch at school” and B is “joins a club”. For a random student, are A and B independent?

    • Independent: 70/100 × 40/100 = 28/100, the share with both
    • Not independent: 70 × 40 = 2,800, not 28
    • Not independent: 70/100 + 40/100 is not 28/100
    • Not independent: lunch might keep students at school for clubs

  12. Use this

    Two-way table of 150 students. Owns a bike and a skateboard: 45. Owns a bike, no skateboard: 45. No bike, owns a skateboard: 15. No bike, no skateboard: 45.

  13. Kira surveyed 150 students and made the two-way table. A is “owns a bike” and B is “owns a skateboard”. For a random student, are A and B independent?

    • Independent: half of bike owners own a skateboard, so about half of the group does
    • Independent: bikes and skateboards are different things
    • Independent: 90/150 and 60/150 are close to each other
    • Not independent: 90/150 × 60/150 = 36/150, but 45/150 are in both
PencilGopencilgo.com

9th grade The counting principle, and are these events independent? worksheet – printable
Print: 123456

About this worksheet

The counting principle, and are these events independent?. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can count the outfits, menus or codes by multiplying the choices at each step, even with no repeats, an "or", or a rule.
  • I can test whether two events are independent by checking whether P(A) × P(B) = P(A and B).
  • I can work back to a missing count or a missing chance by dividing.

Standard: S-CP.B.9 (+, foundation), S-CP.A.2

Words to know

outcome list: Every possible result, one row or one branch each.

counting principle: One choice from each step: multiply the numbers of choices.

no repeats: A choice used once is gone, so the next step has one fewer.

P(A): The chance that event A happens.

P(A and B): The chance that A and B both happen.

independent: P(A) × P(B) equals P(A and B); one event does not change the other's chance.

Common mistakes

Your child added the numbers of choices instead of multiplying them. Try 2 shirts and 3 caps: list the outfits and count all 6.

Your child stopped before the last step of the count. Ask them to name every step before multiplying.

Your child multiplied choices that are alternatives.

What to say

Ask: does one outcome use both choices, or only one?

Questions parents ask

What is the most common mistake with the counting principle, and are these events independent??

Your child added the numbers of choices instead of multiplying them. Try 2 shirts and 3 caps: list the outfits and count all 6.

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

See all Algebra 1

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account